Finite Group DatabasebetaFinite Group Databasebeta| order | 1080 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C3 · Schur multiplier (H2) = C2 |
| unambiguous semidirect product | #67099⋊C3 |
| Fitting | C22×C5×3−1+2 ⋊ C2 |
| Hall | C5×3−1+2 ⋊ D4 |
| Sylow | 3−1+2 ⋊ C22⋊D5 |
| Sylow | C5 ⋊ #611⋊C3 |
106 conjugacy classes of subgroups; only the 36 normal subgroups are shown.
This group has 106 conjugacy classes of subgroups — too many to draw. Only its 36 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 180 |
Polycyclic presentation:
2^2,3,2,3,5,3|e^3=g,b^a=bd,e^a=e^2g^2,f^a=f^4,g^a=g^2,e^c=eg^2119 conjugacy classes — view the full character table.
| maximal subgroup of | D5×#611⋊C3, D4×C5⋊AGL(1,ℤ/9), C22⋊D5×AGL(1,ℤ/9), … |
| maximal normal subgroup of | D5×#611⋊C3, D4×C5⋊AGL(1,ℤ/9), C22⋊D5×AGL(1,ℤ/9), … |
| maximal quotient of | #72254698, C5×#67099⋊C3, #72269531 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1080, 222);